The centers and their cyclicity for a class of polynomial differential systems of degree 7

Rebiha Benterki, Jaume Llibre*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

We classify the global phase portraits in the Poincaré disc of the generalized Kukles systems ẋ=−y,ẏ=x+axy6+bx3y4+cx5y2+dx7,which are symmetric with respect to both axes of coordinates. Moreover using the averaging theory up to sixth order, we study the cyclicity of the center located at the origin of coordinates, i.e. how many limit cycles can bifurcate from the origin of coordinates of the previous differential system when we perturb it inside the class of all polynomial differential systems of degree 7.

Original languageEnglish
Article number112456
Pages (from-to)112456
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume368
DOIs
Publication statusPublished - Apr 2020

Keywords

  • Averaging method
  • Center
  • Cyclicity
  • Hopf bifurcation
  • Limit cycle
  • Phase portrait

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